Squire
Squire isn't very powerful right off the bat. Accumulate increases your attack power by a noticeable amount. Its main hallmark is its ability to wear medium armour, and its decent damage-dealing ability.
Skills:
Throw Stone - This throws a stone for some minor damage, plus an attempted "knockback" equivalent to a weakened Eddy spell.
Dash - Deals damage to a single target. Damage is affected by attack power, and can be very powerful if your physical strength is up to it.
Recover - Fast skill that removes poison, blind, and mute. It can be targetted to heal alies or, if you really want to, mobs.
Accumulate - Increases your attack power equivalent to the Strong spell. Never fight without it up.
Brawler
The Brawler is kind of a late bloomer in terms of power. Blood Lust is like the Thief's Backstab skill in terms of damage, but it berserks you. Rush and Cross Slash can only be used while berserked (you can also wear the Berserker Ring buyable in Narshe for this), but are decent damage-dealing skills. If you like melee damage dealing, at least try out Brawler.
Skills:
Bloodlust - A single-target, powerful physical attack which berserks you and raises physical attack power. It gets better with class level. You can't use this move while berserked, which is annoying at best.
Cooldown - Removes your berserk status out of battle. Nice for having duration berserk not wear off midbattle because you went in with your duration almost gone.
Rush - A powerful physical attack which, if it doesn't kill your attacker, leaves you open to attack by lowering your defense.
Cross Slash - Another damage skill, better than Rush, that carves your name letter by letter into the target's body.
Lancer
Actually, I take it back. The Lancer truly is the class you have to stick with to be good. Using a spear, you may notice your Jump damage is only equivalent to your melee damage at first. Have faith and bear with Lancer, it can only get better (hey, it's hard to get worse than one skill that deals damage equal to your melee).
Skills:
Jump - Moves you out of the room for a short while, then you fall back down and land on the target. Lancer class level affects damage and recharge time, as well as Dragoon class level. This becomes extremely powerful if you put effort into mastering it.
Monk
Simply having Monk improves your Chakra by a fair margin. You'll also notice it adds a randomness to your Chakra. Then you get Suplex. Suplex will be a very, very good source of damage for a very good, long while, if you're of the melee sort. Trust me on this one. Oh, and if you group with someone, Mantra is a fast way of healing your group members without using SP.
Skills:
Kick - Kick is the only "instant damage" skill in the game, but comes at the price of having to recharge after using it. It stuns the target for a brief time and deals little damage.
Pummel - Decent damage skill. It's a bit slow but it gets better as you level your classes.
Mantra - Heals everybody in your party but you for a good amount. Affected by your class level and willpower, goes through Reflect and Wall.
Suplex - Fast, defense-ignoring damage, it's what you'll probably want to use as a fighter from 35-70. Factors in the enemy's level, which does not cap if the target is a mob.
Space Storage - It has hilarious messages and the chance to inflict some rather odd but potent status effects.
Counter-Attack Rate - These increase the base counterattack rate for martial arts classes (including Samurai) from 5% to their respective amounts.
Rogue
Finally, the thief classes can use swords, which you can conveniently Backstab with. Mug is a Steal skill that also adds some damage, and Ambush is a more powerful version of your Backstab skill that adds a steal attempt onto it. Definitely worth getting if you have a fair deal of Dexterity.
Skills:
Mug - Deals damage based on class level and dexterity to target, and attempts to steal from them at the same time. This is a very good way of dealing damage, as it can't miss and isn't affected by defense.
Ambush - Does more damage than Backstab and tries to steal from the target. This fails more than Backstab misses, but failing doesn't start combat.
Black Wizard
If you're a mage and you don't have this, ask yourself why. It has the second-tier elemental spells, which are roughly twice as powerful as their first-tier counterparts... and more accurate as well. If you know of mobs weak to a certain element, the Black Wizard can probably cast the spells that makes it fall down.
Spells:
Blaze/Blizzard/Electricity/Rock/Vile - These deal very nice damage for their cost, and applying them to weaknesses is a good way to kill mobs.
Bio - Deals damage and poisons target. Not bad but not that great either.
Sap - More accurate and powerful than Drain, but it still won't save you if you overhunt.
Psyche - Drains SP from the target, and does it a larger amount than Osmose.
Warp - Warps you to your last save point. Very nice to avoid having to walk back to town.
Blind - Blinds the target, lowering their physical accuracy dramatically.
White Wizard
White magic further develops into stronger cures, a wider variety of buff spells, and the ability to raise people from the dead. It also gains the ability to remove status effects and inflict various others as well.
Spells:
Aid - More powerful than but slower than Cure.
Purify - Removes SP poison. Very little inflicts it, though.
Protect - Increases defense against all elements by a set amount. Quite handy against things that use elemental attacks.
Sight - Removes the Blind status effect. Good, but not something you'll care about mid-combat for yourself.
Regen - Causes the target to slowly regain HP over time. This cancels out poison.
Concentrate - Causes the target to slowly regain SP over time. Handy little spell for keeping your SP up.
Esuna - Removes all negative status effects from the target. Invaluable in certain places.
Mute - Although more things are immune to this the higher level you get, it'll still stop some very annoying spells from hitting you.
Berserk - Berserks the target. It's considered an attack spell, so hitting melee-oriented party members with it requires PK flags all around.
Exit - Same as Warp. Exactly the same.
Life - Raises the target from the dead, making them take no death penalty. People will thank you for using this on them when they die.
Red Wizard
Remember those kids in high school that were the kings of the world, then at the ten-year reunion they were grocery clerks? Well, Red Wizard isn't like them. It gains the ability to wear light armour, and has an assortment of status, healing, and damage magic to help it out. It's not as powerful as other classes, but still decent enough to use with its unique and esoteric effects.
Spells:
Bother - Deals damage to a target's SP. It's surprisingly powerful and repeated use can lock down a mage for good.
Weak - Lowers something's physical attack power, equivalent to a reverse Strong spell. Highly noticeable and very useful.
Bare - Lowers something's magical defense, equivalent to a reverse Shell. This is essential for dealing magical damage to things.
Debility - Lowers something's magical attack power, equivalent to a reverse Power spell. Do I even need to state the obvious?
Prone - Lowers something's physical defense power, equivalent to a reverse Safe spell. Again, I'd be stating the obvious to comment.
Haze - Lowers something's physical accuracy. Not as strong as Blind.
Expose - Lowers something's physical evasion. Handy if you have an axe-wielder in your party.
Ruse/Precision/Peep - See previous commentary.
Dispel - Removes all status conditions from a target (though it can only remove Wall if it's bounced off another Wall first). As the first of two debuffs, it's less powerful than you'd think except to remove things from yourself so you can recast them.
Time Wizard
Time Wizard learns a lot of spells that don't necessarily do a lot of good on their own, but when used judiciously in a party, can be exceptionally powerful. With some niche effects, Time Wizard can be very effective, or downright worthless.
Exit - See White Wizard.
Haste - Speeds up someone. Self-explanatory, and very useful. Keep it up 24/7.
Young - The exact opposite of the Old spell. Minor effects, but every little bit counts.
Float - Defends against earth attacks. This saves equipping a Cherub Down to fight earth-based mobs.
Comet - Second-tier nonelemental damage. Roughly equivalent to Blaze, but more expensive. It also pierces wall, like all the nonelemental damage spells in its line.
Hesitate - Same effect as Pause, but hits all your attackers.
Gravity - Dispels Float. That's about it.
Decelarete - Yet another Slow spell. Same comments apply.
Demi - Deals 15% of a target's current HP to them. While not very useful for normal battles, there is one saving grace to this spell. It can hit bosses.
Shunt - Warps your entire party out of a non-boss fight in a random direction. Slow, but never fails.
Fasten - Removes all haste effects and evasion buffs from a target. Even I admit that it's little more than a filler spell.
Summoner
Summoner goes on to learn a mix of support and offensive summons. The exact list is something I shall not spoil. However, searching all of the realms is highly recommended. Summoner is a very powerful class when its summons are unlocked. For dealing with multiple mobs, Summoner is perhaps the best second-tier class in the game.
Spells:
Secret. Feel free to tell your friends what they are, but I'm not going to spoil anything.
Acrobat
Acrobat is surprisingly powerful at infringing upon a black magic trademark, which is draining something's HP and SP. However, it requires high Charisma to be effective at it. Unlike BLM, though, Acrobat isn't affected by SP or Wall.
Dances:
Jitterbug Duet - Drains HP from a target. Based on charisma, dexterity, and weapon power.
Mystery Waltz - Drains SP from a target. Stat bases as above.
Minstrel
Purely a secondary class, to be certain. Life Song and Angel Song are effective means of healing, but the lack of good gear and weapons hurts it if you're a fighter type.
Skills:
Life Song - Restores HP to you and your party, based on Charisma, and going around Runic and Wall.
Angel Song - See above, but it restores SP instead.
Mechanic
Let's just ignore this class for now. Aside from the Identify buff and Repair success boost, it gives you nothing.
Skills:
None
Chemist
Well, you can wield guns, which has style. You can also mix your own potions to heal yourself, which obviously are better than the dinky Cure3 potions you can buy in shops. Useful class if you can afford to mix potions to cure yourself, or find mixing ingredients abound.
Skills:
Splash - Splashes a potion onto someone, which is basically like forcing them to drink it. Good for splashing status effects.
Taste - Tells you what a potion's effects are.
Mix - Mixes two ingredients together to make a new potion, which can also be mixed. Class levels in both Chemist and Alchemist affect the number of times something can be mixed. A nice skill to have for making your own healing.
Blue Wizard
Blue Wizard has a few spells, with supposedly more on the way but I've not heard anything more than conjecture about what's going in past the list below. Still, it's a pretty damn good class.
Spells:
Goblin Punch - Kind of zeroeth-tier damage to one enemy. It becomes explosively powerful if you're equally levelled to the target, dealing upwards of 10000 damage sometimes. For 5 SP. If you're 100+ and know a mob's level, and want to destroy it quickly, get yourself some experience debt and stay their level for this.
Bloodsuck - Identical to Black Mage's Drain spell.
Gust - First-tier air damage to all enemies, non-diminishing. This is different from Black Mage's Bolt spell in that it's Air damage, not Lightning, and thus uses different weaknesses and resistances.
Moonflute - Area berserk spell that pierces wall. Not that great on most mobs, but it has its uses.
Needler - Exactly 1000 damage to one enemy, no more and no less. This spell does not give JP. For 40 SP, this spell isn't really worth it.
Aero - Second-tier air damage to all enemies, non-diminishing. Same as above for elements.
Aquarake - Second-tier water damage to all enemies, non-diminishing. Not many mobs are weak to it.
Magic Hammer - Halves a target's SP. Multiple uses of this will cripple any mage with the power of geometric reduction.
Revenge - Deals damage equal to your max HP minus your current HP. Only very useful if you have high max HP, but even then fighting at low health is risky.
Hunter
Skin and Debone are how you get some of the more esoteric bounty items, and you get Ambush a lot earlier than with Rogue. Track allows you to find out where in the mud another player is, but Trainer classes can see when you're tracking them. Furthermore, you cannot track a Beast Man, for they are too experienced in the ways of the wilderness to leave any trace of their passing, or something.
Skills:
Aim - A crappy damage skill, which has an exceedingly rare (around 1-2%) chance of dealing a chest shot for massive damage. It gets a damage boost if you have Beast Man, however.
Skin - Removes the skin of a corpse so you can sell it at item shops.
Debone - Take a wild guess.
Spray Shot - Aside from a hilarious but juvenile typo waiting to happen, this does mild damage to the entire room. Not worth using since it's almost strictly worse than X-Fight.
Hunt - A carbon copy of Sneak, it even runs on the same recast timer.
Ambush - See Rogue.
Track - Tells you what room a player's in. You obviously can't track Espers and Admins. Has a high fail rate, and anybody in a Trainer-based class gets a message when they're being tracked. You also can't track Beast Men.
X-Fight - Four weak melee hits to random targets that you're fighting. This is, if used right, an exceedingly powerful melee ability for any class.
On to the third-tier classes.